Rooting technically means to modify your tablet's software so that you have superuser access that gives you the ability to customize and change settings and even install custom Roms such as alternate operating systems, skins or other modifications. In other words when a manufacturer makes a device like a tablet or a phone they usually put an operating system on and lock the device so that you can only access the settings...and use the software...the way they want. But what if for instance you are not happy with the Honeycomb operating system that comes with your Thrive.
There are 'custom Roms', which are other operating systems or other versions of Android that have features and capabilities that the version that came from the factory does not have. For instance...overclocking of the CPU to make the machine faster. 'Rooting' means you've broken the protection mechanisms that Toshiba put on your tablet so that you can tinker and customize your tablet just the way you want...beyond what the manufacturer intended.
Sometimes it even future-proofs your device because you can put a new operating system on your tablet even after the manufacturer has stopped issuing updates. There are also instances when certain modifications and even some programs will only operate after your device is rooted. One example is a a program called 'Honeybar' which allows you to make the little control bar on the bottom of your Thrive's screen disappear with a tap so you can have the full screen for programs and videos. This mod only works if your tablet is rooted.
If you're interesting in more info on why you might want to root your tablet or phone there's a bunch of articles around the web that explain different reasons. One thing you should keep in mind is that rooting your tablet if you're not experienced doing it before does pose some risk if you don't do it right for harming your tablet and making it unusable. It's not common but it does happen. Therefore before you even try it make sure you read several different step by step instructions and follow them to a T. It might even be a good idea the first time to contact someone...a friend, coworker, hobbyist or whoever...someone that has done it before to help out to make sure it's done right. Here are few links to different articles around the web that talk about rooting in general as well as the Thrive specifically. Some of these refer to Android phones instead of tablets but the underlying reasons why you might want to root remain the same regardless of the device. Of course if you decide to proceed make sure you're following a Toshiba Thrive specific set of instructions to root as each device does it slightly differently. In the end it's up to you and if the benefits are worth it to you and if you feel you're comfortable enough with tech gear and hacking that you feel ok to do it.
android authority: beginners-guide-to-root-your-android-phone-or-tablet